In normal stars, dynamos can explain the basics of a stellar magnetic
field, as long as a convective envelope exists in the stellar
interior. But theoreticians have yet to arrive at an adequate, complete,
self-consistent MHD dynamo model of a convective envelope that can
reproduce quantitatively all relevant observations at the same time
(e.g.,
Donati et al. 1997).

The internal structure of a star is reasonably well understood. The
energy released in the interior of stars and in the assemblages of stars
by the action of nuclear and gravitational forces keeps electrically
conducting fluids in turbulent motion. Magnetic field in cool stars
originate from the base of the outer convection zone and migrate
towards the stellar surface through magnetic buoyancy. The magnetic field
entrained in the fluid (ionized gas) is stretched and folded by the
fluid motion (nonuniform rotation and cyclonic convection), gaining
energy in the process (e.g.,
Parker 1983).
Main sequence stars rotate and
have vigorous convective zones (like the Sun), so it follows that there
is a dynamo effect in these stars. The younger stars would seethe with
activity, but their magnetic virility would decline over a period of
108 years (e.g., chapter 21 in
Parker 1979).

An important mechanism to detect stellar magnetic fields at optical
wavelenths is the Zeeman effect, where emitted lines from chemical
elements (e.g., sodium) placed in a magnetic field are splitted into
components and the state of splitting depends on the direction and
strength of the magnetic field. The application of the Zeeman effect to
the optical spectra of certain other classes of star has shown that some
stars do possess magnetic fields. Different absorption lines can be used
for the Zeeman effect, depending on the star's surfae temperature and
hence on the star's spectral type (from hot
O-type and B-type stars, normal A-type,
F-type, and G-type
stars, to cool K-type and M-type stars).

There is typically one large scale dipole and many small localized
surface scale dipoles. Stellar-type magnetic fields often have a basic
large scale dipolar shape near the stellar surface.

Rapidly rotating active stars generally display stellar spots near their
two poles, which is a way to prevent dynamo saturation at high rotation
rate (e.g.,
Solanski et al. 1997).
A dynamo could start saturating when rotation is too high, due to the
back reaction of the magnetic field on the stellar convection and
differential rotation. Slower rotators like the G-type Sun tend to have
their spots near the equatorial plane. The magnetic flux tubes are
rising from deep inside the star, due mainly to magnetic buoyancy and
Coriolis force, and secondarily to magnetic tension and drag.

A detection of a magnetic field in a supposedly 100% convective star or
in a 100% radiative star could be challenging for dynamo theories. Some
low-mass pre-main-sequence objets (such as V410 Tau) are claimed to have
no inner radiative zone, being 100% convective
stars, yet they may have a detectable magnetic field. Some high-mass
pre-main-sequence objects (such as HD 104237) are claimed to have no
convective envelope, being 100% radiative stars, yet they may have a
magnetic field - in such cases, the theoretical work is being
concentrate on the possible presence of a small sub-photospheric layer
with turbulent motions (e.g.,
Donati et al. 1997).

Many stars in a sub-class of spectral type A stars, called
peculiar A
stars or Ap stars, have strong surface magnetic fields.
The magnetic dipole axis are often perpendicular or oblique with respect
to the star's rotation axis, causing a periodic change in the Zeeman
line data.

Thus in an ideal case the "effective" magnetic field B, or
"longitudinal" magnetic field, or the "line-intensity weighted average
over the visible stellar hemisphere of the line-of-sight component of
the magnetic vector", is obtained from Stokes V observations and
should vary with time t during the rotation period p as

where Bpole is the polar magnetic field, i is
the angle between the axis of the magnetic field
dipole and the axis of rotation of the star, and
is the angle
between our line of sight and
the axis of rotation of the star. The observed separation between the
two Zeeman line
components is proportional to the strength of the magnetic field, ie
~
0ge <B>
where 0 is
the normalization wavelength and ge is
the average effective Landé factor
(~ 1, within a factor 2). Current observed effective magnetic field
strengths are ~ 10000 Gauss.

Also in the ideal case the "surface" magnetic field, or the "mean field
modulus", or
the "line-intensity weighted average over the visible stellar hemisphere
of the modulus of
the magnetic vector", is obtained from Stokes I observations at
sufficiently high spectral
dispersion showing the spectral lines splitted into several magnetic
components. The
observed line separation between red and blue components for the Zeeman
doublet of the Fe II line at
6149.258 Åis
given as ~
02g <B> where
0 is the
normalization wavelength
and g is the Landé factor of the split level
2.7 here (e.g.,
Mathys et al. 1997).
Current observed surface magnetic field strengths are ~ 3 kG to 10 kG.

The simultaneous consideration of both the "effective" field and of the
"surface" field is required to derive meaningful constraints on the
geometrical structure of the magnetic field. Such considerations suggest
the following: the magnetic field covers most of the stellar surface,
and the two poles within a star often have different strengths, so one
magnetic pole could be nearer the stellar surface than the other
magnetic pole (e.g.,
Mathys et al. 1997).

The stellar envelope of Ap stars is hot and radiative,
and the
magnetic field is thought to be "fossil" - a remainder of the magnetic
flux previously in the interstellar medium from which the star formed
(e.g.,
Babel and North 1997).

Some stars have a bow shock. Some X-ray emitting gas around peculiar Ap
stars may
be due to a shock near such a star, The dipolar magnetic field of 1000
Gauss is able to bend
the 500 km/s stellar wind towards the magnetic equatorial disk extending
out to 4 stellar radii, resulting in shocked gas near 106 K
(Babel & Montmerle
1997).

Calcium emission lines from stellar spots, where the magnetic field is
strong, will follow a time variation due to the stellar spot
cycle. Since many sun-like, G-type stars show such calcium line
variation over time, it has been inferred that about half of the stars
similar to the Sun may have magnetic fields.

M-type stars, with a smaller mass than the G-type Sun, are rotating
faster than the Sun. All M stars in the Pleiades are rapid
rotators (e.g.,
Jones et al. 1996).
They are thus expected to have (i) a predominently polar magnetic field
and (ii) temporal magnetic activity possibly concentrated near the
stellar poles. Essentially all M stars should display polar,
rather than
equatorial, temporal magnetic activity. A physical result is that
stellar spin-down should be negligible for M stars (e.g.,
Buzasi 1997)

A small number of stars may have a circumstellar disk (not planets)
around, even a long time after star formation. The gas in the
circumstellar disk of
diameter 0.7 AU around the Be star SS2883 has been modeled with a gas
density of 1010 cm-3
and a radial/toroidal magnetic field of 30 Gauss (thin disk) and with a
gas density of 108
cm-3 and a poloidal magnetic field of 14 kiloGauss (thick
disk), as inferred from the
modulation of the RM and DM of the distant orbiting pulsar PSR B1259-63
(e.g.,
Melatos et al. 1995).

A very small number of stars (< 10) are known to have a global
quadrupolar type magnetic field, much like that resulting from two
antiparallel dipoles slightly displaced from each other.

This is the case for the B-type star HD37776 with a diameter
~ 8 × 106 km and a magnetic field reaching 2000 Gauss (e.g.,
Thompson & Landstreet
1985;
Borra & Landstreet
1978).
This is also the case for the Bp star HD133880, whose very
non-sinusoidal magnetic field curve indicates a non-dipolar field
geometry, but rather a predominently quadrupolar magnetic field shape
with a strength ~ 10000 Gauss
(Landstreet, 1990).
The Ap star HD137509 has recently been found to
exhibit such a quadrupolar magnetic shape with a strength ~ 25000 Gauss
(Mathys & Hubrig
1997).

Clearly any mass loss, atmospheric parameter, diffusion velocity, and
other quantity that depends on magnetic field strength and shape will be
affected by this system of quadruple poles. This is even more so if the
magnetic field strength is weak (say 3000 Gauss)
at 2 opposite poles and strong (say 10000 Gauss) at the other 2 opposite
poles.

Donati & Cameron
(1997)
proposed a novel method to analyse Stokes V data, requiring
a single spectral line fit to over 1500 spectral lines from
0.470 µm to
0.710 µm,
assuming
all 1500 line shapes/profiles to be additive, self-similar, and scalable
in width and depth. These and other assumptions (weak magnetic field so
that Zeeman splitting is small
compared to the intrinsic line width; limb darkening is constant with
wavelength) sound rough and should be investigated later. Studying the
rapidly rotating (0.5 day) KO dwarf star AB Dor with this novel method,
Donati & Cameron
(1997)
found (i) 6 active magnetic loops with
B ~ 500 Gauss located at high latitudes on the stellar surface
and corona, and (ii) several
other low-latitude spots. Further analysing their data, they deduced
(iii) some clues for a possible surface toroidal magnetic field at high
latitudes going in opposite direction to the
surface toroidal field at intermediate latitudes, predicting (iv)
another two zones of opposite magnetic polarity in the other stellar
hemisphere; hence they theorized (v) a large scale poloidal magnetic
structure ("octupole") inside the star, giving rise to the four surface
toroidal magnetic structure through the interaction with differential
rotation.